Starting GCSES looking to get into Oxbridge Maths

Hi I’m in year 10 and aiming to apply for maths at Oxbridge. I’m just wondering what I can be doing at this moment to increase my chances of getting into a top university and just improving my mathematical capability overall. I know that the only way to improve at maths is by doing it but I’ve kind of run out of ideas. Like what maths is going to benefit me for studying at these places. Puzzles? Learning high level concepts? Both? Please somebody answer and not just say “focus on your GCSES”. I don’t want to sound obnoxious but GCSE Maths simply doesn’t challenge me and I don’t know what to be doing with my time.

By the way, my current grade is a 9 so I’m also not a charlatan with high expectations. Please help!

Hi I’m in year 10 and aiming to apply for maths at Oxbridge. I’m just wondering what I can be doing at this moment to increase my chances of getting into a top university and just improving my mathematical capability overall. I know that the only way to improve at maths is by doing it but I’ve kind of run out of ideas. Like what maths is going to benefit me for studying at these places. Puzzles? Learning high level concepts? Both? Please somebody answer and not just say “focus on your GCSES”. I don’t want to sound obnoxious but GCSE Maths simply doesn’t challenge me and I don’t know what to be doing with my time.

By the way, my current grade is a 9 so I’m also not a charlatan with high expectations. Please help!

Enter the UKMT challenges - you could get invited to one of the National Maths Summer schools.

Look at answering some of the problems here: https://nrich.maths.org/students/secondary

See if you can borrrow some books like Rob Eastaway 'Why do buses come in threes?', 'How long is a piece of string?'

Talk to your teachers - we have a library of books we lend to keen students.

Do you think your school would let you do an additional maths qualification with your GCSEs - might depend on teachers and how much time they have but it would help you hit the ground running with A-level and also stretch you a bit more if you're finding GCSE too easy. Worth asking at least!

Also have a look at the UKMT maths challenge, not sure if that's something you can only do through schools or just sign up to on your own but I did it at secondary school and sixth form and it was pretty fun, I didn't take it super seriously (or do particularly well lol) but I think it is a nice way to challenge yourself - the maths itself isn't that difficult but applying it in the weird scenarios the questions set up really is! Another thing I remember friends of mine who were really into maths doing is the Mathsbombe - I think it's team based and probably aimed more at year 12/13, but I think they release the problems for anyone to look at so you could try having a go this year (it starts in late January) to see how you find it.

Slight disclaimer that I did Psychology at Oxford and kind of hated A-level maths but a few of my friends were applying for Maths and related subjects at Oxbridge and other similar universities and this is what I remember them doing! I don't know if any of this is the kind of thing that looks good on an application/personal statement or whatever but you don't really need to be worrying about that in year 10, these just might be some more interesting ways to keep doing maths and challenge yourself while you do GCSEs.

Do you think your school would let you do an additional maths qualification with your GCSEs - might depend on teachers and how much time they have but it would help you hit the ground running with A-level and also stretch you a bit more if you're finding GCSE too easy. Worth asking at least!

Also have a look at the UKMT maths challenge, not sure if that's something you can only do through schools or just sign up to on your own but I did it at secondary school and sixth form and it was pretty fun, I didn't take it super seriously (or do particularly well lol) but I think it is a nice way to challenge yourself - the maths itself isn't that difficult but applying it in the weird scenarios the questions set up really is! Another thing I remember friends of mine who were really into maths doing is the Mathsbombe - I think it's team based and probably aimed more at year 12/13, but I think they release the problems for anyone to look at so you could try having a go this year (it starts in late January) to see how you find it.

Slight disclaimer that I did Psychology at Oxford and kind of hated A-level maths but a few of my friends were applying for Maths and related subjects at Oxbridge and other similar universities and this is what I remember them doing! I don't know if any of this is the kind of thing that looks good on an application/personal statement or whatever but you don't really need to be worrying about that in year 10, these just might be some more interesting ways to keep doing maths and challenge yourself while you do GCSEs.

Thanks, my teacher offered for me to do AQA Further Maths and I have done the UKMT before. I will look into the Mathsbombe thing. Thank you such much this was very helpful!

Enter the UKMT challenges - you could get invited to one of the National Maths Summer schools.

Look at answering some of the problems here: https://nrich.maths.org/students/secondary

See if you can borrrow some books like Rob Eastaway 'Why do buses come in threes?', 'How long is a piece of string?'

Talk to your teachers - we have a library of books we lend to keen students.

I've just looked at the UKMT official website and realised it is past the deadline for physical paper purchases and I haven't heard anything from my school about us taking part. Last time we did it, they asked who wanted to do it so they could buy the correct amount of papers, so I'm fairly sure we just aren't doing it this year. How can I sign up myself, and if I can, is it too late?

Ask them on Monday ... they may have ordered them.

Alternatively they may be downloading and printing the papers: https://sites.google.com/ukmt.org.uk/challengehandbook/competition-preparation/downloading-the-question-paper

You can't enter yourself ...

As a supplement to some of the above, for the imc you have https://parallel.org.uk/ which is an online club for y7-11 which is based on ukmt stuff. Previous imcs are online at https://www.drfrostmaths.com/worksheets.php?wdid=44 and there are relevant ukmt and aops books. For me, sitting a challenge is just a scorecard, really any learning/practice you put in is the important part. Similarly the Olympiad should be accessible with some practice. A useful thing to cover for this sort of stuff is some problem solving and I like https://www.worldscientific.com/worldscibooks/10.1142/9478#t=aboutBook. Similarly https://www.openbookpublishers.com/books/10.11647/obp.0168 is a free download which covers relevant maths ideas in a problem based way.

There are a wide variety of popular maths books/youtube/... you can watch, so tomrocks, stewart/sautoy/martin gardner/.... Similarly looking a bit at the history can enliven things a bit. For competitions/problems as well as the ones above, there is a Liverpool one in feb, project Euler if you're into computing, ritangle, various cipher ones. Again, learning from/practice past ones is the key thing.

You asked about whether to look at problems or concepts and much of the above is obviously problems. Having said that, looking at some basic algebra / number theory so divisibility/mod arithmetic, proof, integer/diophantine equations Pythagorean triples... is relevant. So id not be that concerned about any great division between concepts/problems. Just learn something and do a bit of regular practice.